The least action principle in general relativity theory

1998 ◽  
Vol 115 (2) ◽  
pp. 607-611
Author(s):  
M. V. Gorbatenko
Keyword(s):  
General Relativity ◽  
Action Principle ◽  
Relativity Theory ◽  
General Relativity Theory ◽  
Least Action Principle ◽  
Least Action ◽  
The Least Action Principle

scholarly journals A least action principle for interceptive walking

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Soon Ho Kim ◽  
Jong Won Kim ◽  
Hyun Chae Chung ◽  
MooYoung Choi
Keyword(s):  
Social Systems ◽  
Equations Of Motion ◽  
Classical Mechanics ◽  
Action Principle ◽  
Lagrange Equations ◽  
Least Action Principle ◽  
Least Action ◽  
The Least Action Principle ◽  
Principle Of Least Action ◽  
Human Participants

AbstractThe principle of least effort has been widely used to explain phenomena related to human behavior ranging from topics in language to those in social systems. It has precedence in the principle of least action from the Lagrangian formulation of classical mechanics. In this study, we present a model for interceptive human walking based on the least action principle. Taking inspiration from Lagrangian mechanics, a Lagrangian is defined as effort minus security, with two different specific mathematical forms. The resulting Euler–Lagrange equations are then solved to obtain the equations of motion. The model is validated using experimental data from a virtual reality crossing simulation with human participants. We thus conclude that the least action principle provides a useful tool in the study of interceptive walking.

scholarly journals Predicting the peculiar velocities of nearby PSCz galaxies using the Least Action Principle

2001 ◽  
Vol 322 (1) ◽  
pp. 121-130 ◽  
Author(s):  
J. Sharpe ◽  
M. Rowan-Robinson ◽  
A. Canavezes ◽  
W. Saunders ◽  
E. Branchini ◽  
...  
Keyword(s):  
Action Principle ◽  
Least Action Principle ◽  
Least Action ◽  
Peculiar Velocities ◽  
The Least Action Principle

scholarly journals On Hilbert's world-function

1927 ◽  
Vol 113 (765) ◽  
pp. 496-511 ◽  
Keyword(s):  
Dynamical System ◽  
General Relativity ◽  
Minimum Principle ◽  
Relativity Theory ◽  
Field Equations ◽  
General Relativity Theory ◽  
Least Action ◽  
Principle Of Least Action ◽  
The Universe ◽  
World Function

The well-known theorem that the motion of any conservative dynamical system can be determined from the “Principle of Least Action” or “Hamilton’s Principle” was carried over into General Relativity-Theory in 1915 by Hilbert, who showed that the field-equations of gravitation can be deduced very simply from a minimum-principle. Hilbert generalised his ideas into the assertion that all physical happenings (gravitational electrical, etc.) in the universe are determined by a scalar “world-function” H, being, in fact, such as to annul the variation of the integral ∫∫∫∫H√(−g)dx 0 dx 1 dx 2 dx 3 where ( x 0 , x 1 , x 2 , x 3 ) are the generalised co-ordinates which specify place and time, and g is (in the usual notation of the relativity-theory) the determinant of the gravitational potentials g v q , which specify the metric by means of the equation dx 2 = ∑ p, q g vq dx v dx q . In Hilbert’s work, the variation of the above integral was supposed to be due to small changes in the g vq 's and in the electromagnetic potentials, regarded as functions of x 0 , x 1 , x 2 , x 3 .

The Definition of Aesthetics and Beauty

2020 ◽  
pp. 157-178
Keyword(s):  
Action Principle ◽  
Least Action Principle ◽  
Least Action ◽  
The Least Action Principle ◽  
Natural Beauty ◽  
The World ◽  
Definition Of

This chapter proposes the definition of beauty and discusses the levels of beauty and the structure of beauty. This chapter points out that Aesthetics should be a science that studies beauty in general, including natural beauty, artistic beauty, design beauty, and aesthetic feelings. Beauty, just like material and thinking, is the foundation of everything, without which the world won't even exist. Beauty is an evolutionary existence, an objective and natural existence, and an existence of emergence. It is hierarchical, structural, and dynamic, and its core is the “least action principle”.

AB065. Pedestrian modeling using the least-action principle

2018 ◽  
Vol 3 ◽  
pp. AB065-AB065
Author(s):  
Sergio Mejia-Romero ◽  
J. Eduardo Lugo ◽  
Rafael Doti ◽  
Jocelyn Faubert
Keyword(s):  
Action Principle ◽  
Least Action Principle ◽  
Least Action ◽  
The Least Action Principle ◽  
Pedestrian Modeling

scholarly journals Energy-Optimal Electrical-Stimulation Pulses Shaped by the Least-Action Principle

PLoS ONE ◽  
2014 ◽  
Vol 9 (3) ◽  
pp. e90480 ◽  
Author(s):  
Nedialko I. Krouchev ◽  
Simon M. Danner ◽  
Alain Vinet ◽  
Frank Rattay ◽  
Mohamad Sawan
Keyword(s):  
Electrical Stimulation ◽  
Action Principle ◽  
Least Action Principle ◽  
Least Action ◽  
The Least Action Principle
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